How a Sudoku with exactly one solution is made
A Sudoku is only a puzzle if it has one answer. Give it two and the last few cells turn into a coin toss, which is exactly the feeling a logic puzzle is supposed to avoid. Here is how the boards in Lynxy Sudoku are built on your device, and why the difficulty is not quite the same thing as the number of clues.
Step 1: a finished grid
The generator starts from the end. It takes an empty 9×9 grid and fills it with a backtracking solver: pick the empty cell with the fewest legal digits, try those digits in a random order, and back up whenever a cell runs out of options. Because the order is shuffled every time, the result is a different valid grid on almost every run - there are about 6.7 × 1021 of them, so repeats are not a practical worry.
Choosing the most constrained cell first matters more than it sounds. A cell with one possible digit is filled without any guessing, and a cell with two possibilities splits the search in two rather than nine. On a modern phone the whole grid takes a few milliseconds.
Step 2: take clues away, two at a time
Now the finished grid becomes a puzzle by removing digits. The generator walks through the 81 cells in a random order and, for each one, also removes its mirror image through the centre of the board - the cell at 80 − i. That is why Lynxy boards look balanced: if the top-left corner is empty, so is the bottom-right one. Newspaper puzzles have followed this convention for decades, and it costs the solver nothing.
After every removal the generator asks one question: does this grid still have exactly one solution? If yes, the cells stay empty. If no, both digits go back and the walk moves on to the next cell.
Step 3: counting solutions, but only to two
Counting all solutions of a nearly empty grid would take far too long, and it is not needed. The check runs the same solver as in step 1, but it stops the moment it finds a second solution. One solution means the removal was safe; two means it was not, and the exact number beyond that never matters. Most checks finish almost instantly, because a grid with a unique answer is usually forced down a single path within a few branches.
How many clues are left
The walk stops when the board reaches its target:
| Level | Clues left | Mistakes allowed | Points |
|---|---|---|---|
| Easy | about 36 | 3 | 1 |
| Medium | about 30 | 2 | 2 |
| Hard | about 26 | 1 | 3 |
“About” because the walk visits each cell once. If, by the end, no remaining cell can be removed without creating a second solution, the board keeps a few more clues than the target - rare at 36, a little more common near 26.
For the record, the smallest number of clues a proper Sudoku can have is 17. That was settled in 2012 by Gary McGuire's team after an exhaustive computer search showed that no 16-clue puzzle has a unique solution. Our hard boards stay well above that, because very low clue counts tend to produce puzzles that are tedious rather than clever.
Why fewer clues is not always harder
What makes a Sudoku hard is the technique it needs, not how empty it looks. Two boards with 26 clues can feel completely different: one falls apart once you find a couple of hidden singles, the other forces you to spot a pair or an X-Wing before anything moves. The clue count is a decent proxy - fewer givens means fewer easy footholds - but it is only a proxy.
That is the honest limit of a generator that works by clue count. The mistake limit is the other half of the difficulty on Lynxy: one wrong digit ends a hard game, so a lucky guess that happens to work is not a strategy you can rely on.
What this means when you play
- You never have to guess. Every board has exactly one solution, so every empty cell can be deduced from the digits already on the board. If you are stuck, a technique is missing - not information.
- Pencil marks are worth it on hard. With 26 clues there are often only a handful of cells that can be filled directly. Writing candidates down is how you spot the patterns described in our guide to solving techniques.
- The board is yours alone. It is generated in your browser and never sent anywhere, which is also why it is still there when you come back to the tab.